171.—­THE BANNER PUZZLE.

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A Lady had a square piece of bunting with two lions on it, of which the illustration is an exactly reproduced reduction.  She wished to cut the stuff into pieces that would fit together and form two square banners with a lion on each banner.  She discovered that this could be done in as few as four pieces.  How did she manage it?  Of course, to cut the British Lion would be an unpardonable offence, so you must be careful that no cut passes through any portion of either of them.  Ladies are informed that no allowance whatever has to be made for “turnings,” and no part of the material may be wasted.  It is quite a simple little dissection puzzle if rightly attacked.  Remember that the banners have to be perfect squares, though they need not be both of the same size.

172.—­MRS. SMILEY’S CHRISTMAS PRESENT.

Mrs. Smiley’s expression of pleasure was sincere when her six granddaughters sent to her, as a Christmas present, a very pretty patchwork quilt, which they had made with their own hands.  It was constructed of square pieces of silk material, all of one size, and as they made a large quilt with fourteen of these little squares on each side, it is obvious that just 196 pieces had been stitched into it.  Now, the six granddaughters each contributed a part of the work in the form of a perfect square (all six portions being different in size), but in order to join them up to form the square quilt it was necessary that the work of one girl should be unpicked into three separate pieces.  Can you show how the joins might have been made?  Of course, no portion can be turned over.

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173.—­MRS. PERKINS’S QUILT.

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It will be seen that in this case the square patchwork quilt is built up of 169 pieces.  The puzzle is to find the smallest possible number of square portions of which the quilt could be composed and show how they might be joined together.  Or, to put it the reverse way, divide the quilt into as few square portions as possible by merely cutting the stitches.

174.—­THE SQUARES OF BROCADE.

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I happened to be paying a call at the house of a lady, when I took up from a table two lovely squares of brocade.  They were beautiful specimens of Eastern workmanship—­both of the same design, a delicate chequered pattern.

“Are they not exquisite?” said my friend.  “They were brought to me by a cousin who has just returned from India.  Now, I want you to give me a little assistance.  You see, I have decided to join them together so as to make one large square cushion-cover.  How should I do this so as to mutilate the material as little as possible?  Of course I propose to make my cuts only along the lines that divide the little chequers.”

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I cut the two squares in the manner desired into four pieces that would fit together and form another larger square, taking care that the pattern should match properly, and when I had finished I noticed that two of the pieces were of exactly the same area; that is, each of the two contained the same number of chequers.  Can you show how the cuts were made in accordance with these conditions?